If for non-zero x, if \(af\left( x \right) + bf\left( {\frac{1}{x}} \right) = \frac{1}{x} - 25\) where a ≠ b then \(\mathop \smallint \limits_1^2 f\left( x \right)dx\) is

\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {2\;ln\;2 - 25} \right) - \frac{{47b}}{2}} \right]\)

\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {ln\;2 - 25} \right) + \frac{{47b}}{2}} \right]\)

\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {2\;ln\;2 - 25} \right) + \frac{{47b}}{2}} \right]\)

\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {ln\;2 - 25} \right) - \frac{{47b}}{2}} \right]\)

If for non-zero x, if \(af\left( x \right) + bf\left( {\frac{1}{x}} \r

1.	If for non-zero x, if \(af\left( x \right) + bf\left( {\frac{1}{x}} \right) = \frac{1}{x} - 25\) where a ≠ b then \(\mathop \smallint \limits_1^2 f\left( x \right)dx\) is
A.	\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {ln\;2 - 25} \right) + \frac{{47b}}{2}} \right]\)
B.	\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {2\;ln\;2 - 25} \right) - \frac{{47b}}{2}} \right]\)
C.	\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {2\;ln\;2 - 25} \right) + \frac{{47b}}{2}} \right]\)
D.	\(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {ln\;2 - 25} \right) - \frac{{47b}}{2}} \right]\)
Answer» B. \(\frac{1}{{{a^2} - {b^2}}}\left[ {a\left( {2\;ln\;2 - 25} \right) - \frac{{47b}}{2}} \right]\)

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If for non-zero x, if \(af\left( x \right) + bf\left( {\frac{1}{x}} \right) = \frac{1}{x} - 25\) where a ≠ b then \(\mathop \smallint \limits_1^2 f\left( x \right)dx\) is

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